Over the past decade, rapid algorithmic progress has yielded orders of magnitude reductions in the resource overheads of Hamiltonian simulation, bringing the application to the realm of practicality on realistic future quantum hardware. Simulations of non-unitary dynamics, however, have lagged behind. The recent framework of Linear Combinations of Hamiltonian Simulation (LCHS) provides a path to applying well-understood Hamiltonian simulation techniques to these problems, which has led to asymptotic and constant-factor speedups over existing art. In this talk, I will discuss this framework and introduce tools for performing resource estimation within it, including better constant-factor bounds for simulating the unitary dynamics that arise. Further, I will discuss recent advances in data loading via quantum read-only memory, an important problem for the simulation of classical systems on quantum computers.